Asymptotic properties of generalized eigenfunctions for multi-dimensional quantum walks

We construct a distorted Fourier transformation associated with the multi-dimensional quantum walk. In order to avoid the complication of notations, almost all of our arguments are restricted to two dimensional quantum walks (2DQWs) without loss of generality. The distorted Fourier transformation characterizes generalized eigenfunctions of the time evolution operator of the QW. The 2DQW which will be considered in this paper has an anisotropy due to the definition of the shift operator for the free QW. Then we define an anisotropic Banach space as a modified Agmon-H\"{o}rmander's $\mathcal{B}^*$ space and we derive the asymptotic behavior at infinity of generalized eigenfunctions in these spaces. The scattering matrix appears in the asymptotic expansion of generalized eigenfunctions

Restorative Study of 20 Volumes of Kōyagire Kokin-syu : Establishment of the Methodology for Restoring Old Writing

科学研究費助成事業(科学研究費補助金)研究成果報告書：基盤研究(C)2007-2010課題番号：1952009

A case of pulmonary stenosis after a repair for tetralogy of Fallot treated with percutaneous pulmonary valvuloplasty using a triple-balloon technique

SummaryThe patient was a 37-year-old female who had undergone a repair for tetralogy of Fallot (TOF) at the age of 4 years. Postoperative pulmonary stenosis remained, but she continued to be managed medically. Approximately 3 years ago, at the age of 34, she exhibited a worsening of fatigue and dyspnea during exertion (New York Heart Association III), and was therefore hospitalized for a detailed examination. In cardiac catheterization, a right ventricle to pulmonary artery peak-to-peak gradient of about 90mmHg was observed. Since it appeared that medical treatment alone would not sufficiently control her heart failure, pulmonary valvuloplasty using a triple-balloon technique was performed for the pulmonary stenosis. The peak-to-peak gradient immediately after the procedure decreased to 13mmHg. There were no indications of restenosis approximately 6 months after the procedure, and the symptoms of heart failure in her daily life improved thereafter

New Supporting Evidence for the Overdensity of Galaxies around the Radio-Loud Quasar SDSS J0836+0054 at z =5.8

Recently, Zheng et al. (2005) found evidence for an overdensity of galaxies around a radio-loud quasar, SDSS J0836+0054, at z=5.8 (a five arcmin$^2$ region). We have examined our deep optical imaging data (B, V, r', i', z', and NB816) taken with the Suprime-Cam on the Subaru Telescope. The NB816 narrow-band filter (lambda_c = 815 nm and $\Delta\lambda = 12$ nm) is suitable for searching for Ly$\alpha$ emitters at $z\approx 5.7$. We have found a new strong Ly$\alpha$ emitter at $z \approx 5.7$ close to object B identified by Zheng et al. Further, the non detection of the nine objects selected by Zheng et al. (2005) in our B, V, and r' images provides supporting evidence that they are high-z objects.Comment: 5 pages, 1 figure, accepted for PAS

Star-Forming Galaxies at z=0.24 in the Subaru Deep Field and the Sloan Digital Sky Survey

We make a search for Halpha emitting galaxies at z=0.24 in the Subaru Deep Field (SDF) using the archival data set obtained with the Subaru Telescope. We carefully select Halpha emitters in the narrowband filter NB816, using B, V, Rc, i', and z' broad-band colors. We obtain a sample of 258 emitting galaxies with observed equivalent widths of (Halpha+[NII]6548,6584) greater than 12 angstrom. We also analyze a sample of Halpha emitters taken from the Sloan Digital Sky Survey (SDSS) to constrain the luminous end of Halpha luminosity function. Using the same selection criteria as for the SDF, and after excluding AGNs, we obtain 317 Halpha emitting star-forming galaxies. Combining these two samples of Halpha emitters found in both SDF and SDSS, we derive a Halpha luminosity function with best-fit Schechter function parameters of alpha = -1.31^+0.17_-0.17, log phi^* = -2.46^+0.34_-0.40 Mpc^-3, log L^* = 41.99^+0.08_-0.07 ergs s^-1. An extinction-corrected Halpha luminosity density is 4.45^+2.96_-1.75 x 10^39 ergs s^-1 Mpc^-3. Using the Kennicutt relation between the Halpha luminosity and star formation rate, the star formation rate density in the survey volume is estimated as 0.035^+0.024_-0.014 M_sun yr^-1 Mpc^-3. The angular two-point correlation function of Halpha emitters over 875 arcmin^2 at z = 0.24 is well fitted by a power-law form with w(theta) = 0.047^+0.017_-0.013 theta^-0.66 +- 0.08, corresponding to the correlation function of xi(r) = (r/2.6^+1.0_-0.8 Mpc)^(-1.66 +- 0.08). The small correlation length of Halpha emitters may imply the weak clustering of active star-forming galaxies.Comment: 22 pages, 10 figures, PASJ, Vol.60, No.6 in pres

Genetics of Endometrial Cancers

Endometrial cancers exhibit a different mechanism of tumorigenesis and progression depending on histopathological and clinical types. The most frequently altered gene in estrogen-dependent endometrioid endometrial carcinoma tumors is PTEN. Microsatellite instability is another important genetic event in this type of tumor. In contrast, p53 mutations or Her2/neu overexpression are more frequent in non-endometrioid tumors. On the other hand, it is possible that the clear cell type may arise from a unique pathway which appears similar to the ovarian clear cell carcinoma. K-ras mutations are detected in approximately 15%–30% of endometrioid carcinomas, are unrelated to the existence of endometrial hyperplasia. A β-catenin mutation was detected in about 20% of endometrioid carcinomas, but is rare in serous carcinoma. Telomere shortening is another important type of genomic instability observed in endometrial cancer. Only non-endometrioid endometrial carcinoma tumors were significantly associated with critical telomere shortening in the adjacent morphologically normal epithelium. Lynch syndrome, which is an autosomal dominantly inherited disorder of cancer susceptibility and is characterized by a MSH2/MSH6 protein complex deficiency, is associated with the development of non-endometrioid carcinomas

Strong Emission-Line Galaxies at Low Redshift in the Field around the Quasar SDSSp J104433.04-012502.2

We discuss observational properties of strong emission-line galaxies at low redshift found by our deep imaging survey for high-redshift Ly alpha emitters. In our surveys, we used the narrowband filter, NB816 (lambda_center=8150A with FWHM = 120A), and the intermediate-band filter, IA827 (lambda_center = 8270A with FWHM = 340A). In this survey, 62 NB816-excess (> 0.9 mag) and 21 IA827-excess (> 0.8 mag) objects were found. Among them, we found 20 NB816-excess and 4 IA827-excess Ly alpha emitter candidates. Therefore, it turns out that 42 NB816-excess and 17 IA827-excess objects are strong emission-line objects at lower redshift. Since 4 objects in the two low-z samples are common, the total number of strong low-z emitters is 55. Applying our photometric redshift technique, we identify 7 H alpha emitters at z~0.24, 20 H beta-[OIII] ones at z~0.65, and 11 [OII] ones at z~1.19. However, we cannot determine reliable photometric redshifts of the remaining 17 emitters. The distributions of their rest frame equivalent widths are consistently understood with recent studies of galaxy evolution from z~1 to z~0.Comment: 28 pages, 8 figures, PASJ, Vol. 58, No. 1, in pres